In his book, Practical Ethics, Peter Singer makes this claim about Divine Command Ethics
Some theists say that ethics cannot do without religion because the very meaning of ‘good’ is nothing other than ‘what God approves’. Plato refuted a similar claim more than two thousand years ago by arguing that if the gods approve of some actions it must be because those actions are good, in which case it cannot be the gods’ approval that makes them good. The alternative view makes divine approval entirely arbitrary: if the gods had happened to approve of torture and disapprove of helping our neighbours, torture would have been good and helping our neighbours bad. (p. 3)
In the beginning of this passage, Singer makes out Divine Command Theory (DCT) to be a claim about the meaning of the word “good.” To say something is “good” is simply to say that it is “approved by God.” The relationship between “good” and “approved by God” is one of identity. One simply means the other. However, Singer then goes on to state the standard Euthyphro dilemma, which challenges DCT by asking “Is something good because God commands it, or does God command it because it’s good?” If something is good because God commands it, then God could have commanded rape and torture and that would have been good, which goes against our intuitions. If God commands something because it is good, then something is good prior to God commanding it, so God cannot be appealed to as a source of moral facts.
Notice that the Euthyphro dilemma presupposes that there is an asymmetrical relationship between “goodness” and “approved by God.” One is ontologically and causally prior to the other. However, the identity theory says that there is a symmetrical relationship between “goodness” and “approved by God.” One simply means the other, neither is ontologically or causally prior to the other. Considering these facts, the Euthyphro dilemma does not provide a challenge to the view that “good” and “approved by God” are identical.
Imagine I said “‘Bachelor simply’ means ‘unmarried man'”, and you responded by saying “But is he a bachelor because he is unmarried or is he unmarried because he is a bachelor?” The question does not make sense since neither “bachelor” nor “an unmarried man” is ontologically or causally prior to the other. “Bachelor” is simply another way of saying “an unmarried man.” In the same way, the Euthyphro dilemma does not provide a challenge to the view that “good” is identical to “approved by God” since the dilemma presupposes that their relationship is causal.
(1) “The Premature Dismissal of Voluntarism” Colloquium: The Australian and New Zealand Theological Review (November 2010).